com.numericalmethod.suanshu.stats.hmm.rabiner

Class HmmXi

java.lang.Object

com.numericalmethod.suanshu.stats.hmm.rabiner.HmmXi

All Implemented Interfaces:

java.io.Serializable

public class HmmXi
extends java.lang.Object
implements java.io.Serializable

ξ is the probability of the system being in state s_i at time t and state s_j at time t+1, given the model and observation sequence.

ξ_t(i, j) = P(q_t = s_i, q_t+1 = s_j | Ω, λ)

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
HmmXi(HiddenMarkovModel model) Construct the xi matrices generator.

Method Summary

Modifier and Type	Method and Description
Matrix[]	xi(int[] observations) Get the ξ matrices, where for 1 ≤ t ≤ T - 1, the t-th entry of ξ is an (N * N) matrix, for which the (i, j)-th entry is ξt(i, j).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

HmmXi

public HmmXi(HiddenMarkovModel model)

Construct the xi matrices generator. Generate the xi matrices of a (discrete) HMM, where for 1 ≤ t ≤ T - 1, the t-th entry of xi is an (N * N) matrix, for which the (i, j)-th entry is xi_t(i, j).

Parameters:

model - a (discrete) hidden Markov model

Method Detail

xi

public Matrix[] xi(int[] observations)

Get the ξ matrices, where for 1 ≤ t ≤ T - 1, the t-th entry of ξ is an (N * N) matrix, for which the (i, j)-th entry is ξ_t(i, j).

Parameters:

observations - an integer array of observation symbols (length = T). Each symbol is a positive integer less than or equal to M (the number of observation symbols per state).

Returns:

the ξ matrices